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If x = log(a)^(bc), y = log(b)^(ca) and ...

If `x = log_(a)^(bc)`, `y = log_(b)^(ca)` and `z = log_(c)^(ab)` then show that `frac(1)(x+1)+frac(1)(y+1)+frac(1)(z+1) = 1`, `[abc ne 1]`

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Let's simplify : 2frac(1)(3) div 1frac(1)(6) div 1frac(1)(4)

Let's solve : frac(1)(3)(x-2) + frac(1)(4) (x + 3) = frac(1)(5)(x + 4) + 15

UNITED BOOK HOUSE-Hare School, Question Paper -Exercise
  1. Show that, if n be any positive integer greater than 1, then (2^(3n) -...

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  2. If x = log(2a)^(a), y = log(3a)^(2a) and z = log(4a)^(3a) show that xy...

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  3. If x = log(a)^(bc), y = log(b)^(ca) and z = log(c)^(ab) then show that...

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  4. If none of the figures, 3, 4, 5, 6, 7 be repeated, how many different ...

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  5. State and prove that Cauchy-Schwarz inequality.

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  6. If a, b, c be three unequal sides of a triangle show that frac(1)(b+c-...

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  7. If n be a positive integer greater than 1, prove that (frac(n+1)(2))^n...

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  8. If a, b, c one positive numbers satisfying 4ab + 6bc + 8ca = 9 find th...

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  9. Distinguish between attribute and variable.

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  10. Find the arithmetic mean and median for first n natural numbers.

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  11. Find the AM of 5, 55, 555,…………….upto n times.

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  12. If P(A) = 1/2, P(B) = 2/3 then prove that 1/6 le P(A nn B) le 1/2

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  13. If 9 biscuits of different types be distributed among 3 children, find...

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  14. Show that overset(n)underset(i=1)sum (xi - A)^2 is minimum when A = ba...

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  15. If y = (x-a)/b, then prove that Sy = frac(Sx)(|b|)

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  16. Prove that P(A uu B) = P(A) + P(B) - P(A nn B)

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  17. The variance of 1, 2,…………..n is 24. Find n.

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  18. For 10 values of X, it is given that sumu = 4 and sum u^2 = 144, where...

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  19. Two groups of 15 and 22 values have variances 9 and 16 respectively. I...

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  20. For a set of an positive quantities prove that AM ge GM ge HM.

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